I know of mobile game whales, but not their etymology. Philipp on the Arqade StackExchange explained:
The term “Whale” is borrowed from the casino industry, where it is used to describe a rich gambler who bets extraordinarily large amounts of money. Just like in the game industry, casinos want to “catch” the most high-betting whales, because they provide a lot of income for comparably little expense. Casinos often go out of their way to form personal connections with whales and provide them with personalized service to ensure their loyalty and make sure they lose their money in their casinos and not those owned by the competition. Some game companies in the microtransaction business are also known to do this.
The casinos, in turn, took the term from the Poker community which has a tradition of using fish-themed terms for different categories of players, like “fish” for weak players and “shark” for strong players who prey on the “fish” in order to take their money. A “whale” is what every “shark” hopes to find: a very large fish* who has a lot of money and likes to play high-stakes games despite not being skilled enough to compete in them.
*Yes, I know that whales are mammals and not fish.